Big W has removed T-shirts bearing an "AUSTRALIA EST 1788" logo from its Australia Day product range after discount supermarket Aldi bowed to online pressure on Wednesday and canned plans to sell similar shirts.

It comes as Fairfax Media revealed the T-shirts pulled by Aldi had been approved by the federal government.

It is unclear if the Big W shirts were also approved by the government.

Aldi was criticised on Wednesday for a range of promotional T-shirts branded with "AUSTRALIA EST 1788" logos, advertised online.

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The design sparked an online clamour. People took to social media to label the range racist and culturally insensitive to Australia's indigenous people, who inhabited the continent for tens of thousands of years before the arrival of the First Fleet from England in 1788.

The seven designs had been approved by the Department of the Prime Minister and Cabinet in July 2013, under strict guidelines regarding products bearing the image of the Australian flag.

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A department spokesman said staff had been concerned with the representation of the flag, not external elements.

"In this case, the department provided approval on the basis that the flag was reproduced completely and accurately."

A spokeswoman for Woolworths confirmed on Thursday the shirts would not be sold.

Aldi also apologised for the range via its Twitter account following calls for the shirts to be removed from shelves from numerous social media users, including Sunshine Coast University lecturer Matt Mason.

"This is historically wrong and racist," Mr Mason posted. "Remove them from sale."

One online commentator, known as Conrad Henley-Calvert on Twitter, went so far as to write directly to Aldi explaining the reason for his anger and asking it to pull the T-shirt from its range.

"In 1788 Australia was already inhabited by the world's oldest continuous living culture, and many of the descendants of those first Australians view 26 January as the anniversary of an invasion, not of the founding of a new nation," his letter of complaint read.

Former Race Discrimination Commissioner Tom Calma said he did not believe the design was "intentionally racist".

"What we can say is that it is not accurate, is bad taste and does not in itself lead to an understanding of Australia's history and heritage," he said. "In the lead-up to Australia Day it is important that we educate the community, the nation and the international community about what Australia Day celebrates."